Читать книгу Antenna and EM Modeling with MATLAB Antenna Toolbox - Sergey N. Makarov - Страница 15

A small antenna operating at f = 10 MHz uses a thin copper wire with the diameter D of 0.25 mm and with the wire length l of 1 m. Calculate antenna loss resistance R_L.

Solution: The DC resistance of the wire is given by

(1.3)

where σ is the material conductivity and A is the wire cross section. However, we cannot use this formula since most of the high‐frequency current flows in a thin skin layer around the wire. The correct result has the form:

(1.4)

where P is wire perimeter and μ₀ is vacuum permeability. A short MATLAB script given below accomplishes the task and gives R_L approximately equal to 1 Ω. This value may be comparable to the radiation resistance of a small antenna, and may even exceed it.

clear all; mu = 4*pi*1e-7; % Vacuum permeability, H/m sigma = 5.7e7; % Copper conductivity, S/m D = 0.25e-3; % Diameter, m l = 1; % Length, m f = 10e6; % Frequency, Hz RHF = l/(pi*D)*sqrt(mu*2*pi*f/(2*sigma)) % Loss resistance